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March 9th, 2019, 06:13 AM  #1 
Newbie Joined: Apr 2016 From: Wonderland Posts: 23 Thanks: 0  Finding square root of matrix without eigenvector
A is a 2x2 matrix. (0 2) (2 0) Find the square root of this matrix. I managed to find one of the square root, because I know A is a 90degree anticlockwise rotation stretched by a factor of 2. So I just have to "half" that operation and I get (1 1) (1 1) However, there is another matrix which is the square root of A and I'm struggling to find it. How can I find it without using eigenvectors/eigenvalues? 
March 9th, 2019, 08:44 AM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,373 Thanks: 1276 
what if we do two rotations the other direction? $A = 2 Rot\left(\dfrac \pi 2\right)$ $\sqrt{A} = \sqrt{2} Rot\left(\dfrac{3\pi}{4}\right)$ $\sqrt{A} = \sqrt{2}\begin{pmatrix}1 &1\\1 &1\end{pmatrix}$ 
March 11th, 2019, 04:05 AM  #3 
Newbie Joined: Apr 2016 From: Wonderland Posts: 23 Thanks: 0 
Thank you romsek. I managed to solve it with your advice and got (1 1) (1 1) 

Tags 
eigenvector, finding, matrix, root, square 
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